Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0911.5500 · Journal of Physics Conference Series

Search for electron liquids with non-Abelian quasiparticles

Arkadiusz Wójs

Published Mar 1, 2010• 0 citations
arXivHTMLPDF

Abstract

We use exact numerical diagonalization in the search of fractional quantum Hall states with non-Abelian quasiparticle statistics. For the (most promising) states in a partially filled second Landau level, the search is narrowed to the range of filling factors 7/3 < v e < 8/3. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at v e = 5/2 (paired Moore–Read "pfafian" state) and 12/5 (clustered Read–Rezayi "parafermion" state). Outside of this range, the noninteracting composite fermion model with four attached flux quanta is validated, yielding the family of quantum liquids with fractional, but Abelian statistics. The borderline v e = 7/3 state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.

DOI
10.1088/1742-6596/213/1/012022

Related papers

Fractional Quantum Hall States with Non-Abelian Statistics

Gunnar Möller, Arkadiusz Wójs, Nigel R. Cooper

Using exact numerical diagonalization we have studied correlated many-electron ground states in a partially filled second Landau level.We consider filling fractions ν = 1/2 and 2/5, for which incompressible quantum liquids with non-Abelian anion statistics have been proposed.Our calculations include finite layer width, Landau level mixing and arbitrary deformation of the interaction pseudopotential.Computed energies, gaps, and correlation functions support the non-Abelian ground states at both ν = 1/2 ("Pfaffian") and ν = 2/5 ("parafermion" state).

Acta Physica Polonica A•Nov 1, 2009•0 citations

Numerical evidence for non-Abelian quantum liquids in the lowest Landau level

Arkadiusz Wójs

Signatures of non-Abelian statistics are sought in correlated liquids of composite fermions (CFs) responsible for a ``second generation'' of fractional quantum Hall effect. The hierarchy stems from the zero-energy state of a model CF interaction by means of a flux attachment procedure converting this uniquely correlated state of ``first-generation'' CFs to a filled shell of second-generation ${\text{CF}}^{\ensuremath{\ast}}$'s. Quasiholes of this state do not obey Abelian statistics. The hierarchy is confirmed numerically, including known states at filling factors ${\ensuremath{\nu}}_{e}=4/11$ and 3/8 and a hypothetical state at ${\ensuremath{\nu}}_{e}=9/25$.

Physical Review B•Jan 27, 2009•5 citations

Condensation of Nonabelian Moore-Read Quasiholes in Correlated Composite Fermion Liquids

D. Wodziński, Arkadiusz Wójs, J. J. Quinn

Two-and three-body correlation functions (number of pairs or triplets vs. relative angular momentum) of electrons or Laughlin quasielectrons (i.e., composite fermions in their first excited Landau level) are studied numerically in several fractional quantum Hall liquids.It is shown directly that the νe = 4/11 liquid (corresponding to a ν = 1/3 filling of composite fermions in their first excited Landau level) is a paired state of quasielectrons, hence interpreted as a condensate of "second-generation" quasiholes of Moore-Read ν = 1/2 state of composite fermions.

Acta Physica Polonica A•Sep 1, 2006•0 citations

Second generation of incompressible quantum liquids in the fractional quantum Hall effect

Arkadiusz Wójs

We study 'second generation' of fractional quantum Hall states which contain a partially filled composite fermion (CF) Landau level (LL). We explain the role of CF-CF interaction in the incompressibility of the underlying quantum electron liquid. In particular, using exact diagonalization on a Haldane sphere, we determine two- and three-body CF correlation functions for these liquids and show that the CFs form a paired state (instead of a Laughlin liquid) when filling v = 1/3 of their second LL. At v = 1/2 we show that the CFs group into even larger clusters rather than form a Moore—Read paired state. We also address the problem of spin polarization of interacting CFs and predict transition to the partially unpolarized ground state in sufficiently narrow quantum wells and/or weak magnetic fields.

Journal of Physics Conference Series•Mar 1, 2008•0 citations

The fractional quantum Hall effect at filling factor 5/2: numerically searching for non-abelian anyons

Michael R Peterson

We review some theoretical progress towards understanding the origin of the fractional quantum Hall effect at filling factor 5/2 using numerical techniques. The leading candidate thought to describe the physics is the Moore-Read Pfaffian state which supports non-abelian anyonic excitations. Interestingly, these excitations have possible applications in topologically protected quantum information processing. Specifically, we discuss how the finite-thickness of realistic quasi-two-dimensional systems stabilizes the Moore-Read Pfaffian in the fractional quantum Hall effect at 5/2 and the use of bilayer systems in the second Landau level to investigate the possible quantum phase transition between abelian and non-abelian fractional quantum Hall states.

Journal of Physics Conference Series•Dec 20, 2012•5 citations

Tracing non-Abelian anyons via impurity particles

Niccolò Baldelli, Bruno Juliá-Díaz, Utso Bhattacharya +2 more

Non-Abelian excitations are an interesting feature of many fractional quantum Hall phases, including those phases described by the Moore-Read (or Pfaffian) wave function. However, the detection of the non-Abelian quasiparticles is challenging. Here, we consider a system described by the Moore-Read wave function and assume that impurity particles bind to its quasiholes. Then, the angular momentum of the impurities, reflected also by the impurity density, provides a useful witness of the physics of the non-Abelian excitations. By demanding that the impurities are constrained to the lowest Landau level, we are able to write down the corresponding many-body wave function describing both the Moore-Read liquid and the impurities. Through Monte Carlo sampling, we determine the impurity angular momentum, and we show that it suggests a quantum-statistical parameter $\ensuremath{\alpha}=a\ensuremath{\nu}\ensuremath{-}b+P/2$ for the quasiholes, where $\ensuremath{\alpha}$ ranges from 0 for bosons to 1 for fermions. A reasonable agreement with the Monte Carlo results is obtained for $a=1/4$, $b=1/8$, and $P=0,1$ depending on the parity of the particle number in the Moore-Read liquid. This parity dependence of the angular momentum serves as an unambiguous demonstration of the non-Abelian nature of the excitations. In addition to the studies of excitations in the Moore-Read liquid, we also apply our scheme to Laughlin liquids, for which we focus on interacting bosonic impurities. With this, the impurities themselves form Laughlin states, which allows for a study of hierarchical fractional quantum Hall states.

arXiv:2102.02072•Physical review. B./Physical review. B•Jul 16, 2021•21 citations
We use exact numerical diagonalization in the search of fractional quantum Hall states with non-Abelian quasiparticle statistics. For the (most promising) states in a partially filled second Landau level, the search is narrowed to the range of filling factors 7/3 < v e < 8/3. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at v e = 5/2 (paired Moore–Read "pfafian" state) and 12/5 (clustered Read–Rezayi "parafermion" state). Outside of this range, the noninteracting composite fermion model with four attached flux quanta is validated, yielding the family of quantum liquids with fractional, but Abelian statistics. The borderline v e = 7/3 state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.
Using exact numerical diagonalization we have studied correlated many-electron ground states in a partially filled second Landau level.We consider filling fractions ν = 1/2 and 2/5, for which incompressible quantum liquids with non-Abelian anion statistics have been proposed.Our calculations include finite layer width, Landau level mixing and arbitrary deformation of the interaction pseudopotential.Computed energies, gaps, and correlation functions support the non-Abelian ground states at both ν = 1/2 ("Pfaffian") and ν = 2/5 ("parafermion" state).
Signatures of non-Abelian statistics are sought in correlated liquids of composite fermions (CFs) responsible for a ``second generation'' of fractional quantum Hall effect. The hierarchy stems from the zero-energy state of a model CF interaction by means of a flux attachment procedure converting this uniquely correlated state of ``first-generation'' CFs to a filled shell of second-generation ${\text{CF}}^{\ensuremath{\ast}}$'s. Quasiholes of this state do not obey Abelian statistics. The hierarchy is confirmed numerically, including known states at filling factors ${\ensuremath{\nu}}_{e}=4/11$ and 3/8 and a hypothetical state at ${\ensuremath{\nu}}_{e}=9/25$.
Two-and three-body correlation functions (number of pairs or triplets vs. relative angular momentum) of electrons or Laughlin quasielectrons (i.e., composite fermions in their first excited Landau level) are studied numerically in several fractional quantum Hall liquids.It is shown directly that the νe = 4/11 liquid (corresponding to a ν = 1/3 filling of composite fermions in their first excited Landau level) is a paired state of quasielectrons, hence interpreted as a condensate of "second-generation" quasiholes of Moore-Read ν = 1/2 state of composite fermions.
We study 'second generation' of fractional quantum Hall states which contain a partially filled composite fermion (CF) Landau level (LL). We explain the role of CF-CF interaction in the incompressibility of the underlying quantum electron liquid. In particular, using exact diagonalization on a Haldane sphere, we determine two- and three-body CF correlation functions for these liquids and show that the CFs form a paired state (instead of a Laughlin liquid) when filling v = 1/3 of their second LL. At v = 1/2 we show that the CFs group into even larger clusters rather than form a Moore—Read paired state. We also address the problem of spin polarization of interacting CFs and predict transition to the partially unpolarized ground state in sufficiently narrow quantum wells and/or weak magnetic fields.
We review some theoretical progress towards understanding the origin of the fractional quantum Hall effect at filling factor 5/2 using numerical techniques. The leading candidate thought to describe the physics is the Moore-Read Pfaffian state which supports non-abelian anyonic excitations. Interestingly, these excitations have possible applications in topologically protected quantum information processing. Specifically, we discuss how the finite-thickness of realistic quasi-two-dimensional systems stabilizes the Moore-Read Pfaffian in the fractional quantum Hall effect at 5/2 and the use of bilayer systems in the second Landau level to investigate the possible quantum phase transition between abelian and non-abelian fractional quantum Hall states.
Non-Abelian excitations are an interesting feature of many fractional quantum Hall phases, including those phases described by the Moore-Read (or Pfaffian) wave function. However, the detection of the non-Abelian quasiparticles is challenging. Here, we consider a system described by the Moore-Read wave function and assume that impurity particles bind to its quasiholes. Then, the angular momentum of the impurities, reflected also by the impurity density, provides a useful witness of the physics of the non-Abelian excitations. By demanding that the impurities are constrained to the lowest Landau level, we are able to write down the corresponding many-body wave function describing both the Moore-Read liquid and the impurities. Through Monte Carlo sampling, we determine the impurity angular momentum, and we show that it suggests a quantum-statistical parameter $\ensuremath{\alpha}=a\ensuremath{\nu}\ensuremath{-}b+P/2$ for the quasiholes, where $\ensuremath{\alpha}$ ranges from 0 for bosons to 1 for fermions. A reasonable agreement with the Monte Carlo results is obtained for a=1/4a=1/4a=1/4, b=1/8b=1/8b=1/8, and P=0,1P=0,1P=0,1 depending on the parity of the particle number in the Moore-Read liquid. This parity dependence of the angular momentum serves as an unambiguous demonstration of the non-Abelian nature of the excitations. In addition to the studies of excitations in the Moore-Read liquid, we also apply our scheme to Laughlin liquids, for which we focus on interacting bosonic impurities. With this, the impurities themselves form Laughlin states, which allows for a study of hierarchical fractional quantum Hall states.